A196204 - OEIS

%I #8 Mar 01 2018 05:34:50

%S 3,5,8,11,18,28,43,67,105,164,257,404,636,1003,1585,2509,3978,6317,

%T 10046,15998,25509,40723,65083,104122,166737,267242,428678,688151,

%U 1105443,1776907,2857894,4598959,7404324,11926298,19217795,30978737,49954191

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,4,1 for x=0,1,2,3,4.

%C Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 4's, every 4 is next to 4 1's.

%C Column 2 of A196210.

%H R. H. Hardin, <a href="/A196204/b196204.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-4) - a(n-5).

%F Empirical g.f.: x*(1 + x + x^2)*(3 - 4*x - x^2) / ((1 - x - x^2)*(1 - x - x^3)). - _Colin Barker_, Mar 01 2018

%e Some solutions for n=4:

%e ..0..0....0..1....1..0....1..0....0..1....0..0....1..1....1..0....0..1....0..0

%e ..0..0....0..1....1..0....1..1....0..1....1..1....0..0....1..0....1..1....0..0

%e ..0..0....1..1....1..1....0..1....0..1....1..1....0..0....1..0....1..0....0..0

%e ..1..1....1..0....0..1....0..1....0..1....0..0....0..0....1..0....1..0....0..0

%Y Cf. A196210.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 29 2011